numpy.allclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)[source]#

Returns True if two arrays are element-wise equal within a tolerance.

The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b.


The default atol is not appropriate for comparing numbers with magnitudes much smaller than one (see Notes).

NaNs are treated as equal if they are in the same place and if equal_nan=True. Infs are treated as equal if they are in the same place and of the same sign in both arrays.

a, barray_like

Input arrays to compare.


The relative tolerance parameter (see Notes).


The absolute tolerance parameter (see Notes).


Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array.

New in version 1.10.0.


Returns True if the two arrays are equal within the given tolerance; False otherwise.

See also

isclose, all, any, equal


If the following equation is element-wise True, then allclose returns True.:

absolute(a - b) <= (atol + rtol * absolute(b))

The above equation is not symmetric in a and b, so that allclose(a, b) might be different from allclose(b, a) in some rare cases.

The default value of atol is not appropriate when the reference value b has magnitude smaller than one. For example, it is unlikely that a = 1e-9 and b = 2e-9 should be considered “close”, yet allclose(1e-9, 2e-9) is True with default settings. Be sure to select atol for the use case at hand, especially for defining the threshold below which a non-zero value in a will be considered “close” to a very small or zero value in b.

The comparison of a and b uses standard broadcasting, which means that a and b need not have the same shape in order for allclose(a, b) to evaluate to True. The same is true for equal but not array_equal.

allclose is not defined for non-numeric data types. bool is considered a numeric data-type for this purpose.


>>> np.allclose([1e10,1e-7], [1.00001e10,1e-8])
>>> np.allclose([1e10,1e-8], [1.00001e10,1e-9])
>>> np.allclose([1e10,1e-8], [1.0001e10,1e-9])
>>> np.allclose([1.0, np.nan], [1.0, np.nan])
>>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)